[Risolto] Calcola il valore delle seguenti espressioni in N applicando, ove possibile, le proprieta`delle potenze

14)

$2^7·(2^5)^2 : (2^4)^4 + 3^9·(3^2)^3 : (3^4)^3$ = 

= $2^7·2^{5·2} : 2^{4·4} +3^9·3^{2·3} : 3^{4·3}$ =

= $2^7·2^{10} : 2^{16} +3^9·3^6 : 3^{12}$ =

= $2^{7+10-16} +3^{9+6-12}$ =

= $2^1+3^3$ =

= $2+27$ =

= $29$

15)

$[(16 : 8 : 2)^3·(24 : 6 : 2)^4 ·2^7] : (2^3)^2$ =

= $[1^3·2^4·2^7] : 2^{3·2}$ =

= $[1·2^{4+7}] : 2^6$ =

= $2^{11} : 2^6$ =

= $2^{11-6}$ =

= $2^5$ =

= $32$

16)

$(16^4 : 8^3) : 2^4 +27^2 : 81$ =

= $(2^4·2^4·2^4·2^4 : 2^3·2^3·2^3) : 2^4 +3^2·9^2 : 9^2$ =

= $(2^{4+4+4+4-3-3-3}) : 2^4 +3^2·9^{2-2}$ =

= $2^{16-9} : 2^4 +3^2·9^0$ =

= $2^7 : 2^4 +3^2·1$ =

= $2^{7-4} +3^2$ =

= $2^3+3^2$ =

= $8+9$ =

= $17$

17)

$\{[36 : (6 : 2)]^3·12^4\} : (12^3)^2-[(36 : 6 : 2)^3·3^4] : (3^2)^3$ =

= $\{[36 : 3]^3·12^4\} : 12^{3·2} -[3^3·3^4] : 3^{2·3}$ =

= $\{12^3 · 12^4\} : 12^6 -[3^{3+4}] : 3^6$ =

= $12^{3+4} : 12^6 -3^7 : 3^6$ =

= $12^7 : 12^6 -3^{7-6}$ =

= $12^{7-6} -3^1$ =

= $12^1-3$ =

= $12-3 = 9$

2^7 * 2^(5*2) / 2^(4*4) + 3^9 * 3^(2*3) / 3^(4*3)

2^(7+10) / 2^16 +3^(9+6) / 3^12

2^(17-16) + 3^(15-12)

2^1+3^3 

2+27 = 29 

((16 / (8*2))^3 * (24/(6*2))^4 * 2^7) / 2^(3*2)

(1^3 * 2^4*2^7) / 2^6

1*2^(7+4) / 2^6 

2^(11-6) 

2^5 = 32

(2^(4*4) / 2^(3*3)) / 2^4 + 3^(3*2) / 3^4 

2^(16-9) / 2^4 + 3^(6-4)

2^(7-4) + 3^2

2^3 + 3^2

8 + 9 = 17